A Method for Discriminating Between Models Describing Compositional Data

Shen, S. M.

doi:10.2307/2335994

Cited by 4 publications

(6 citation statements)

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“…Let 9 0 be the true value of 9 under H f and y 0 be the true value of y under H g . Following Shen [24], we propose to measure the "closeness" of H g to H f as the infimum of If g (9 0 ,y) over y. Assuming that If g (6 0 ,y) has a unique minimum at yj(9 o ), the closeness of H g to Hf can then be measured by 2 For y^(9 0 ) to exist it is necessary that the probability density function under H g is nonzero in the range of variations of Y under H f .…”

Section: Nested and Non-nested Hypothesesmentioning

confidence: 99%

Global and Partial Non-Nested Hypotheses and Asymptotic Local Power

Pesaran¹

1987

Econom. Theory

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This paper addresses two related issues in the literature of non-nested hypotheses testing. Firstly, by means of a measure of “closeness” of probability density functions, it shows how any two hypotheses can be placed into the nested and the non-nested categories with the latter category being subdivided further into “globally” and “partially” non-nested hypotheses. Secondly, by emphasizing the distinction between a “local null” and a “local alternative,” the paper shows that only in the case of partially non-nested hypotheses is it possible to specify local alternatives. In this case the paper derives the asymptotic distribution of the Cox test statistic under local alternatives and shows that it is distributed as a normal variate with a mean which is directly related to the measure of “closeness” of the alternative to the null hypothesis.

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Section: Nested and Non-nested Hypothesesmentioning

confidence: 99%

Global and Partial Non-Nested Hypotheses and Asymptotic Local Power

Pesaran¹

1987

Econom. Theory

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“…For any investigation of complete sub composition independence it would appear that the following sequence is the best that can be recommended. First test for Dirichlet form along the lines of Shen (1982) or even by informal comparison of the tr', L d and Ad fits, as in Table 1. In the likely event of rejection, since compositional data seldom appear to be so strongly structured, test for logistic-normality.…”

Section: Subcompositional Independencementioning

confidence: 99%

“…The fact that the D d and L d classes are identified with parametric hypotheses within the Ad model encourages the view that it should now be possible to construct simple tests of Dirichlet and logistic-normal forms based on the generalized loglikelihood statistics IA -ID and IA -IL , respectively. In particular, we would then be able to avoid the complications of separate family testing in comparing Dirichlet with logistic-normal form, as in Shen (1982). Unfortunately these parametric hypotheses correspond to sets on the boundary of the parameter space of the Ad model so that the Wilks (1938) approximation (4.4) is not directly applicable.…”

Section: A Generalized Lognormal-gamma Distribution With Compositionamentioning

confidence: 99%

A General Class of Distributions on the Simplex

Aitchison

1985

Journal of the Royal Statistical Society Series B: Statistical Methodology

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SUMMARY The Dirichlet class of distributions on the simplex is overstructured for practical work because of its many strong independence properties. A persistent problem of distribution theory has thus been to extend this class to include members free of these independence properties. An alternative approach has been the recent introduction of the logistic‐normal class which contains members with and without the independence properties. Unfortunately, this class is separate from the Dirichlet class and so cannot sustain discussion of some strong forms of independence. These difficulties are overcome in this paper by the introduction of a more general class which includes as special cases the Dirichlet and logistic‐normal classes. The role of this new class in relation to the analysis of compositional data, in particular the investigation of independence hypotheses, is discussed and illustrated.

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“…For the moment, I feel a more hopeful line of enquiry is to investigate more fully the nature of the differences between logisticnormal and Dirichlet distributions. Aitchison and Shen (1980) showed that for many Dirichlet distributions there is a closely approximating logistic normal distribution; this fact has indeed been exploited in the construction of a test of Dirichlet against logistic-normal form by Shen (1982). Some of the tests of independence such as complete subcompositional independence when they lead to rejection also automatically reject the Dirichlet form.…”

Section: The Trick In Handlingmentioning

confidence: 99%

Discussion of Professor Aitchison's Paper

1982

Journal of the Royal Statistical Society Series B: Statistical Methodology

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A Method for Discriminating Between Models Describing Compositional Data

Cited by 4 publications

References 0 publications

Global and Partial Non-Nested Hypotheses and Asymptotic Local Power

Global and Partial Non-Nested Hypotheses and Asymptotic Local Power

A General Class of Distributions on the Simplex

Discussion of Professor Aitchison's Paper

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